Path-Integral Monte Carlo. This technique is used to study atoms deposited on surfaces.
A good reference for this technique is our paper:

"Path-integral Monte Carlo simulation of the second layer of 4He adsorbed on graphite".
M. Pierce and E. Manousakis
 Phys. Rev. B 59, 3802 (1999) [View:PDF (1 MB)]

Green's function Monte Carlo.  This techniques is used to study the ground state
of correlated systems. A recentl publication which describes the technique and gives
references is the following.

"Green's function Monte Carlo for Lattice Fermions: Application to the t-J Model".
C. S. Hellberg and E. Manousakis, Phys. Rev. B 61,   11787 (2000).

We also use Monte Carlo methods for classical models.
If  the order parameter has been correctly identified, such models
can describe the critical properties of quantum phase transitions
within the context of Landau-Ginzburg theory of phase transitions.
Related references  can be found in

"Finite-size scaling in two-dimensional superfluids"
 N. Schultka and E. Manousakis
 Phys. Rev. B 49, 12071-12077 (1994)  [View Page Images, PDF (639 kB)]

We also use exact diagonalization techniques.
See for example the following publication.

"Stripes and the t-J Model "
 C. Stephen Hellberg and E. Manousakis
 Phys. Rev. Lett. 83, 132 (1999). [View: PDF (1MB)]

While the solution provided by such method is exact for the
ground state or a few low-lying excited states, only small
size systems can be studied by the method.
Since we are interested for properties in the thermodynamic
limit, the results obtained with this technique have to be taken
with great caution.